Topography measuring apparatus

ABSTRACT

A contour measuring apparatus and method of using the apparatus is disclosed to measure the three-dimensional contour of a surface. A multi-point light source directs a plurality of light beams onto the surface to be measured. The light beams are reflected through a lens onto a photodetector to produce electro-optically measurable optical images. A structure is provided to determine the local radius of curvature of the surface at each desired point of incidence of individual light beams and the three-dimensional surface contour of the surface being measured. A calibration device is provided to reduce instrument errors of the apparatus. The calibration device includes a calibration surface with a known contour to be positioned in substitution of the surface being measured. The apparatus includes a structure to sequentially determine and store a memory of the location of the calibration surface and to compare the reflection of the light from the calibration surface as well as the surface being measured to determine the contour of the surface being measured.

This application is a continuation of U.S. application Ser. No. 125,240,filed Nov. 15, 1987, now U.S. Pat. No. 4,902,123 entitled TOPOGRAPHYMEASURING APPARATUS.

BACKGROUND OF THE INVENTION

While the invention is subject to a wide range of applications, it isparticularly suited to measure the three-dimensional contour of asurface. In particular, this invention relates to that aspect ofophthalmic diagnosis which is concerned with measurement of thethree-dimensional contour of the anterior surface of the cornea. Thismeasurement discloses abnormalities in the cornea which may havedeleterious effects upon vision or quantifies progress of ophthalmicsurgery, such as laser-aided radial keratotomy or laser ablation of theexternal surface of the cornea with penetration into the stroma andvolumetric removal of tissue, whereby the external corneal surface ischaracterized by a sculptured, new curvature having improved opticalproperties.

Devices variously called corneascopes or keratometers have beendeveloped for topographic analysis of the cornea. Such devices havefound acceptance as means for measuring corneal curvature in preparationfor prescribing a contact lens to be worn over the measured cornea toreduce certain visual defects, or for use in other ophthalmicapplications. The prior art for these devices entails photographic (asin U.S. Pat. No. 3,797,921, Kilmer, et al.) or electro-optical (see U.S.Pat. No. 4,572,628, Nohda) recording of cornea-reflected images ofilluminated objects comprising several concentric rings, or multiplediscrete light sources arranged in the form of concentric rings, on aflat surface normal to the optical system axis or on a concave surfacesymmetrically disposed with respect to that axis. If the cornea isspherical, the reflected images of these ring-shaped objects are equallyspaced, continuous or intermittent, concentric ring-shaped patterns. Ifthe cornea surface is rotationally symmetrical but not spherical, theresultant ring images are less equally spaced; the inequality of spacingis thus a measure of nonsphericity of the cornea surface. If the corneasurface is astigmatic, as is frequently the case, the ring-shaped imagesreflected by that cornea will appear elliptical, and the eccentricity ofthe pattern is related to the change in curvature of the cornea surfacebetween various sectional meridians. This eccentricity, and hence theastigmatism of the surface, can be measured by careful analysis of animage of the ring pattern. The orientation of the major and of theelliptical pattern relative to the eye indicates the orientation of theprincipal axes of the observed astigmatism. If the cornea has beenwarped or distorted by injury, by disease or by prior surgicalprocedures, such as radial keratotomy or imperfect closure of incisionsmade during cataract or other surgery, the magnitudes of these surfacedefects can also be measured.

In each of these described cases, the desired end result is (1) atabular or graphic representation of the surface optical power (in unitsof diopters) at various points over the visually used, central portionof the cornea (typically 3 to 7 mm in diameter), and (2) computedaverage values for these parameters over the area of interest. Becauseof the tendency for the eye to become astigmatic, or non-rotationallysymmetrical, comparisons of surface radius or power are frequently madefor various azimuthal meridians about the visual axis. Instrument errorsintroduced by the apparatus and systematic or random errors introducedby the method of use are preferably minimized in order to minimize theoverall measurement error. Prior art devices for accomplishing thesemeasurements have been found lacking in regard to one or more of thefollowing attributes: accuracy, ease of use, and time required to obtainthe desired tabular or graphical output. None of these devices iscompatible with use in situ and in close temporal alignment withsurgical laser sculpturing of the cornea to produce desired netcurvature changes to improve vision.

BRIEF STATEMENT OF THE INVENTION

It is an object of the invention to provide a method and means forimproving the accuracy and speed with which the topography of theanterior surface of the cornea can be measured.

It is a specific object to meet the above object by incorporating aself-calibration capability which ensures that the instrument error ofthe measurement is small.

It is another object to incorporate a simple means for achieving properlocation and orientation of the eye under test with respect to thediagnostic apparatus.

A further specific object is to make possible the measurement of cornealradius, and thus optical power, at individual small, localized areas onthe surface.

Another object is to provide an in situ means for observing the exteriorof the eye and for measuring the topography of the cornea surface atselected times before, during and after performance of surgicalprocedures such as are taught by pending L'Esperance, Jr. patentapplications including Ser. No. 691,923, now U.S. Pat. No. 4,669,466Ser. No. 748,358 now U.S. Pat. No. 4,665,913, Ser. No. 891,169 and Ser.No. 891,285 now U.S. Pat. No. 4,732,148. Those applications cover theablation of the cornea with penetration into the stroma and volumetricremoval of corneal tissue through controlled application of radiationfrom an ultraviolet laser, or similar procedures utilizing radiation oflonger wavelength such as an infrared laser operating at about 2.9micrometers.

The invention achieves the foregoing objects by analyzing the pattern ofimages of an array of light points specularly reflected from the surfacebeing measured such as the convex surface formed by a cornea beingmeasured for diagnostic purposes or, for example, a spherical ball ofknown radius of curvature used for apparatus calibration purposes. In apreferred embodiment, the apparatus is capable of interfacing directlywith apparatus as described by Telfair, et al., in pending patentapplications Ser. No. 938,633 now U.S. Pat. No. 4,911,711 and Ser. No.009,724, so as to permit diagnostic evaluation of a given cornea inconjunction with surgical sculpturing of the same cornea with laserradiation to improve its optical properties.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be illustratively described for preferred and otherembodiments, in conjunction with the accompanying drawings, in which:

FIG. 1 is a simplified block diagram to show the functionalrelationships of generalized optical, mechanical and electricalcomponents of topography-measuring apparatus of the invention;

FIG. 2 is a diagram of principal optical components of FIG. 1, includingan array of multiple light sources;

FIG. 3 is a diagram showing certain geometric relationships that arepertinent to the optical arrangement of FIG. 2;

FIG. 4A is a simplified optical diagram of apparatus of FIG. 1, arrangedin a calibrating mode, and FIG. 4B is a similar but fragmentary diagramto illustrate a modification;

FIGS. 5A and 5B are respectively front-end and longitudinal-sectionviews, to an enlarged scale, for a calibration element in FIG. 4B, andFIG. 5C is a modified calibration element.

FIG. 6 is a representation, in a radial-plane projection, for anillustrative distribution of multiple light sources in the array of FIG.2;

FIG. 7 is a diagram to illustrate use of the invention in conjunctionwith apparatus for surgical sculpture of the cornea;

FIG. 8 is an optical diagram to show another application of theinvention;

FIG. 9 is a further development of FIG. 4A incorporating means tomeasure alignment of the eye calibration device relative to thediagnostic apparatus;

FIG. 10 shows the typical appearance of the visual field of the focusalignment sensing means in the calibration mode;

FIG. 11 shows the typical appearance of the visual field of the focusalignment sensing means in the operational mode; and

FIG. 12 is a simplified diagram relating the focus alignment sensingmeans to a laser sculpturing apparatus.

DETAILED DESCRIPTION OF THE INVENTION

A contour measuring apparatus 9 to measure the three-dimensional contourof a surface 13 is disclosed. The apparatus includes a multi-point lightsource 11 to direct a plurality of individual light beams 10 onto thesurface 13. A photodetector 19 produces electro-optically measurableoptical images. A lens 15 is disposed between the surface 13 and thephotodetector 19 to focus the reflected beams of light 14 from thesurface being measured 13 onto the photodetector 19 to form themeasurable optical images. A signal switch 21, a frame grabber 23, andcomputer means 24 are in electrical communication with saidphotodetector 19 for determining both the local radius of curvature ofthe surface 13 at each desired point of incidence of the individuallight beams and the three-dimensional contours of the surface 13. Acalibration device 70 is provided to reduce instrument errors of theapparatus 9. The calibration device 70 includes a calibration surface 72with a known contour to be positioned in substitution of the surface 13being measured. Components 21 and 23 sequentially determine and store inmemory the location on said calibration surface 71 of each image ofindividual light points. Means 24 further determine the contour of thesurface 13 being measured from a differential evaluation of thereflection of each light point image from the surface 13 being measuredin comparison to the reflection of each light point image from thecalibration surface 71 with a known contour.

In FIG. 1, the invention is shown as an apparatus 9 for producing andinterpreting images reflected from a surface under test. An array 11 oflight sources is activated by a power supply 12, and multiple diverginglight beams 10 from the array are intercepted by a contoured surface 13under test; contoured surface 13 acts as a mirror to reflect light beams14 into a lens 15 which, in turn, focuses those light beams 16 throughan aperture or iris 17. The beams 18 emerging from aperture 17 are thenfocused onto the sensitive surface of a photo-detecting means 19.Electrical output signals 20 generated by means 19 are directed by asignal switch 21 to a frame grabber 23 which produces a time-sequencedseries of electrical signals representative of the spatial distributionof energy in the image formed by lens 15. These electrical signals canbe displayed as a real time video image in a display apparatus 22.Alternatively or in addition, the electrical signals can be stored indigital form by a frame grabber 23, for further analysis by a computer24 and/or for supply to display means 22 or print-out means 25. Specialalgorithms stored in computer 24 permit computation of the radius ofcurvature, and hence of the optical power, of contoured surface 13 atthe point of incidence on said surface of the beam from any one lightsource in the array 11. Means 26 allows the optical alignment of thesurface 13 relative to the axis of lens 15 to be measured.

Further detail as to function of the involved optical system of theinvention is shown in FIG. 2, wherein the array 11 comprises a pluralityof individual light emitting diodes (LEDS) disposed on a nominallyspherical surface 11A, of known contour, having its center C₁ on theoptical axis 27 of the system. Preferably, the surface 11A is nominallyspherical; however, it is within the terms of the invention for thesurface 11A to be of any desired shape. Although the array 11 of lightsources preferably is comprised of LEDs, it is also within the terms ofthe present invention to construct the array 11 of any type of lightsources, such as a plurality of fiber optics. The center C₂ of a convexsurface 28, equivalent to surface 13 in FIG. 1, under test also lies onthe axis 27 but does not necessarily coincide with C₁. One of the beams10 is the divergent beam 29 from a typical LED 30 which is redirected,upon reflection from surface 28, as a more divergent beam 31 of thebeams 14 into the aperture of a lens 32. The lens 32 is preferablycentered on axis 27 and located at an appropriate distance downstreamfrom surface 28. Through the image-forming properties of lens 32, animage of the typical LED 30 is produced at some point on thephotocathode 33 of a conventional photo-detecting device 19 which may bea vidicon-type image tube; alternatively, device 19 may be an array ofdiscrete detectors such as a charge coupled device (CCD). Typically, thephotocathode of such an image tube or array would have usable aperturedimensions of about 6.6×8.8 mm and would be sensitive to the visiblelight emitted by the light source 11. Because of the inherent rotationalsymmetry of the various optical and electro-optical components about theaxis 27, the image of the entire array 11 typically lies within a circleinscribed within the rectangular usable aperture of the photocathode. Itshould be noted that the photodetector means 19 is in no way limited tothe indicated light source or particular dimensions, in that larger orsmaller devices of like or different nature may be accommodated byselection of the specific type of photodetector 19 and by appropriatelyscaling the size of the image.

A feature of the invention is the inclusion of an aperture such as iris34 located on the axis 27, offset from lens 32 at a distancesubstantially equal to the back focal length (BFL) of the lens 32, thusplacing iris 34 at the focal point of the lens. The opening of iris 34is constrained to always be small enough that it, rather than theaperture of lens 32, determines the angular size of the conical beam 31'of beam 18. The iris 34 acts as the aperture stop of the system andcontrols the cone angle of the individual beams 14, 16, 18, 31', 31 and29 as well as the size of the area "a" on test surface 28 whichcontributes light from the typical LED 30 to the corresponding imagepoint on photodetecting means 19. Since iris 34 is located at the focalpoint of lens 32, light rays 31'A passing centrally through the iris, atany angle "b" with respect to axis 27, must propagate parallel to axis27 in the space between test surface 28 and lens 32. These rays 31'A,called principal rays, are then said to be telecentric in the objectspace of lens 32, and the aperture stop 34, i.e., the iris, is atelecentric stop. The opening in the iris 34 can be small since the LEDsare intrinsically very bright and the image sensor is very sensitive toincident light. All the rays in the beam from a given LED are thereforephysically near each other and all closely approximate the path of theappropriate principal ray.

The fact that the principal rays from all LEDs in the array 11 travelparallel to axis 27, after reflecting from surface 28, allows use of asimple mathematical process to independently compute the average radiusof surface 28 over each of the small localized areas of dimension "a"centered about the intercept points of the principal rays on surface 28.

FIG. 3 illustrates the applicable geometrical condition. It may be notedthat surface 28 is located at an axial distance d₁ from surface 11A andthat the principal ray 29 from a typical LED 30 (here assumed to be apoint source of light at P₂) intercepts surface 28 at a height Y₁ fromthe axis 27 and proceeds to lens 32 as ray 29' parallel to said axis.Ray 29' becomes ray 29" beyond lens 32 and passes through focal point Fen route to point P₃ at the image plane within the image sensor 19. Theradial distance Y₃ of P₃ from the axis 27 is related to Y₁ by thelateral magnification ratio inherent in the lens 32. A method fordetermining this magnification ratio is described later in thisdescription.

The law of reflection at an optical surface requires the path of ray 29from P₂ to P₁ to be such that (a) its extension (dashed line) throughsurface 28 and (b) the extension (dashed line) of reflected ray 29' areboth tangent (at P₅ and P_(4') respectively) to a circle constructedconcentric with surface 28. The perpendicular distance from tangentpoint P₄ to center C₁ thus equals the perpendicular distance fromtangent point P₅ to that same center. For convenience, both of thesedistances will be referred to as "r", which may be expressed: ##EQU1##where: A=Y₁ -Y_(2')

B=X₂ -X_(1') and

C=X₂ Y₁ -X₁ Y₂

and X_(c') Y_(c) are the coordinates of center C₁ measured from X and Yaxes through origin "0" at surface 11A. Since ray 29' is parallel toaxis 27, as shown in FIG. 3, r also equals Y₁. In the nominal case,Y_(c) =0, since C₁ lies on the X axis.

As mentioned in connection with FIG. 1, the image on the photodetector19 can be analyzed mathematically. A frame of multiple LED images can bestored digitally by frame grabber 23 for subsequent analysis in computer24 and display at 22. The results of the analysis can be tabulated andvarious representations of the surface contour printed by printer 25.The information needed to compute the radius of curvature of the surface28 at various points comprises the radial distance Y₃ for each of theimages of the LEDs in array 11. Since the magnification ratio of lens 32can be determined, the corresponding heights Y₁ can be computed.

When the coordinates of P₂ and of C₁ and the coordinate of P₁ are known,the unique value of X₁ can be computed from the quadratic equation:##EQU2## where: D=A (2 Y₁ -A),

E=2 A (A X_(c) -X_(c) Y₁ -X₂ Y₁), and

G=A² (Y₁ ² -X_(c) ²)+2 A X_(c) X₂ Y₁

Once X₁ and Y₁ are known, the radius R₁ at P₁ can be computed from theexpression: ##EQU3##

In general, the axial distance d₁ between the surfaces 11A and 28 can bemeasured by standard means. Hence,

    X.sub.c =d.sub.1 +R.sub.1                                  (4)

Since radius R₁ is initially unknown, an iterative procedure may be usedwherein a reasonable value for R₁ is chosen and substituted intoEquation 4 to give a first approximation for X_(c). Then, values of thecoefficients A, D, E and G are determined, and a first approximationvalue for R₁ is computed from Equation 3. Successive computations giveprogressively more precise values for R₁ ; the iterative process isstopped when the desired precision is achieved.

This mathematical process is repeated for each LED image, and the localradius of the cornea is computed, for each of the various locationsintercepted by narrow beams from the individual LEDs. The average radiusof the surface, the extreme long and short radii of said surface, thedioptric equivalent of each of these radii, and the difference inaverage optical powers in the directions of the principal astigmaticmeridians, as well as the azimuthal orientations of said meridians, canthen be determined using methods of analytic geometry.

The location for each luminous point P₂ must be known in order for thelast described computational process to be used. These locations can bedetermined by directly measuring the coordinates of each LED source ofthe array 11. Alternatively, and preferably, this location can bedetermined with a calibration device 70. The calibration device includesa surface 71 of known contour. This surface 71 may comprise a sphericalsurface. A preferred technique of performing the calibration ofapparatus 35 is accomplished by inserting a substantially sphericalmember 72 having a spherical surface 28' of precisely known radius intothe apparatus 36. The spherical member 72 is located with its center onaxis 27 at distance d₁ from surface 11A, as shown in FIG. 4A. Thespherical member 72 can be positioned in the axial direction and in twotransverse directions with respect to topography measuring apparatus 35,using adjusting means 36 which may typically comprise athree-dimensional translation stage. Proper centering is indicated byequality the dimensions S₁ and S₂ to each other in the plane of FIG. 4A,as well as in the plane which includes axis 27 and is perpendicular toFIG. 4A. Adjustments to locate surface 28' at the specified distance d₁from the spherical LED locus (surface 11) can be accomplished by thelinear adjustment means of fixture 36. Once initially aligned, a conicalseat 37 and a spring-loaded clamping means 38 provide a convenient andreliable means for relocating the spherical member 72 at its prescribedlocation, whenever calibration is to be rechecked.

In order to use the reflecting spherical member 72 as a calibrationmeans, or to use the corneascope-type apparatus 35 to determine thetopography of a cornea under test, the magnification of lens 32 must beknown. This parameter can be measured as indicated in FIG. 4B, where afiducial target member 39 is inserted in the adjustable fixture means 36against the seat 37 at an axial distance d₃ from surface 11A. Then, adetermination is made of the size of the corresponding image of thesurface of target 39 on photodetecting means 19. The ratio of themeasured image dimension to the actual object dimension is themagnification of the optical system, or lens 32. Typically, the absolutevalue of said magnification is about 0.4 to 0.6 times.

The ideal value of d₃ is slightly greater than d₁ since target surface41 should be located essentially at the same distance from lens 32 asthe image of the LEDs reflected by convex surface 28. The latter imageis virtual and located at a distance behind said surface 28 given by theexpression:

    d.sub.2 =(R.sub.1 d.sub.1)/(2d.sub.1 +R.sub.1)             (5)

Typically, for d₁ =100 mm and R₁ =8 mm, d₂ =4.2 mm and d₃ =d₁ +d₂ =104.2mm. This location of the fiducial target surface 41 ensures that theimages at the photodetector 19 of the LEDs and of the fiducial targetwill both be in focus.

By virtue of the telecentric nature of the optical system in objectspace of the lens 32, the magnification is essentially constant formoderate variations (of the order of a few millimeters) in the distanced₁. Since the location of a given point on the photosensitive surface ofphotodetecting means 19 is generally derived by measuring the distanceof the point in units of pixel (picture element) widths horizontally andpixel heights vertically from some reference (such as a corner of therectangular raster), and since the dimensions of a typical pixel may bedifferent in these directions, the linear magnifications in these twodirections may differ from each other. The measured values wouldgenerally be stored in computer memory for use at appropriate timesduring the subsequent computations.

The fiducial target 39 may be any of a variety of types such as two ormore seperated marks 73 so designed as to reflect or absorb lightthereby becoming visible due to contrast against the background formedby the underlying surface of the target substrate. Since magnificationcan vary azimuthally about the axis 27 of an optical system, it isadvisable to have dual fiducial marks on each of at least two mutuallyperpendicular intersecting diameters. In a preferred simple embodiment,a circular fiducial ring 40 is scribed or otherwise marked on thefiducial target substrate 39. The ring 40 is then located so as to beconcentric with the axis 27, as indicated in FIGS. 5A and 5B. Thefiducial ring 40 may be generated on a flattened surface 41 of anotherwise spherical target body 72, e.g., a flat locally ground on atooling or bearing ball. It can then easily be seated against theconical seat 37 of the adjusting means 36 of FIG. 4B, thereby assuringproper centering with respect to the spherical LED locus 11 and to theaxis 27. The depth of material removed in generating the flattenedsurface of the fiducial target on a sphere of radius R₁ is equal to theaforementioned dimension d₂.

As indicated in FIG. 5C, the functions of the spherical reflectingcalibration surface 28' and of the fiducial target 39 can be combined asat 39B by suitably machining a spherical ball.

In a calibrating use, the LED sources are illuminated and thecorresponding locations of the images at the image sensor 19 determinedin the same manner as for the corneal reflections previously described.After converting these images to corresponding heights Y₁, the actual Xand Y coordinates of the points P₂ for all the LEDS can be computed.This is the self-calibration process referred to as one object of theinvention.

The method for accomplishing this computation also relies upon the lawof reflection at surface 28 and mathematical expressions derived fromanalytic geometry, as follows:

    Y.sub.2.sup.4 +IY.sub.2.sup.3 +JY.sub.2.sup.2 +LY.sub.2 +M=0;(6)

where:

H=4 K₂ ² +K₃ ²

I=(4 K₂ K₃ R₂ +2 K₃ K₄ +8 K₁ K₂) / H

J=(4 K₁ ² +4 K₁ K₃ R₂ +4 K₂ K₄ R₂ +2 K₃ K₅ +K₄ ²) / H

L=(4 K₁ K₄ R₂ +4 K₂ K₅ l R₂ +2 K₄ K₅) / H

M=(4 K₁ K₅ R₂ +K₅ ²) / H

K₁ =(X_(c) -X₁) Y₁ ²

K₂ =(X₁ -X_(c)) Y₁

K₃ =Y₁ ² -X_(c) ² +2 X_(c) X₁ -X₁ ²

K₄ =2 (X_(c) ² Y₁ -X_(c) X₁ Y₁ -Y₁ ³)

K₅ =Y₁ ⁴ +X₁ ² Y₁ ² -X_(c) ² Y₁ ²

Once the Y₂ values have been computed, it is a simple matter to computethe corresponding X₂ values from the expression: ##EQU4## where R₂ isthe known radius of curvature of the spherical locus of all the LEDsources (i.e., points P₂).

This feature of the present invention allows the corneascope to becalibrated thereby negating the deleterious effects of unavoidablemanufacturing uncertainties in locations of the LED light sources usedin calculating the corneal radius. By accomplishing this calibrationperiodically, instrument errors can be reduced to a minimum, and theresultant precision in measuring radius of curvature and diopritic powerat a given point on the cornea is improved significantly over thatachieved with prior art methods and apparatus.

In order to provide radius information at an adequate number of pointsover the circular area of interest on the cornea (typically of 5 to 7millimeters diameter, centered on the optical axis of the eye) forophthalmic diagnosis purposes, the light-source array 11 preferablyincludes many individual point light sources. FIG. 6 illustrates such anarray comprising 64 LEDS arranged as 4 rows of 16 LEDS each crossing theaperture of the array, along meridians oriented at 45-degree intervalsof azimuthal angle. The LEDS are located on a concave spherical surfaceto minimize the overall size of the apparatus while providing therequired angular inclination of narrow beams from the individual sourcesto the subsequent optical elements in the system. It will be understoodthat additional light sources can be included along each meridian in thearray, or additional meridians can be added in total or in part, if moreinformation about the corneal contour is needed; conversely, fewer lightsources may be used if less information is needed. In an alternateembodiment, a full complement of many light sources could be installed,but specific geometric groupings of sources could be selected by asuitable switching arrangement (not shown) to fit the need of aparticular measurement to be accomplished at any time, thereby reducingthe overall time required for processing and analysis of the data.

As was pointed out earlier in this description, the physical aperturediameter of the telecentric stop (iris) 34 can be quite small and yetallow sufficient light to pass through the system to produce detectableimages on the photosensing means 19. Calculations pertinent to aparticular embodiment of the invention indicate that, for image qualityreasons, the image-forming beam should have an effective relativeaperture no larger (i.e., no faster) than f/13. This has a secondaryeffect upon the performance of the image-forming system in that itsignificantly increases the depth of field for the LEDs and allows sharpimages thereof to be formed at all points within the field of view. Someprior art systems used for this purpose have exhibited degraded imagesharpness at edges of their field of view due to uncorrected aberrationsrelated to the large effective relative aperture used therein.

The radial distance Y₂ indicated for a typical LED in FIG. 6 correspondsto the Y coordinate of point P₂ in FIG. 3, and it will be noted thatradial separations (Y₂) between LEDs along any meridian are notconstant. This circumstance reflects the preferred condition of equalradial separations (Y₁) of adjacent incidence points P₁ for theprincipal rays on surface 28. If the surface 28 is spherical, thecorresponding radial separations of image points in the image plane atphoto-detecting means 19 also are equal. While not essential to thefunction of the apparatus, this equality of image spacing facilitatesdetection of surface 28 irregularities, including astigmatism, when thecomposite image of the entire LED array is observed on the display 22 ofFIG. 1 or is shown in hard copy produced by printer 25.

In FIG. 7, the invention is shown in simplified form, interfacingdirectly (via a fold mirror 42) with laser-sculpturing apparatus 61 ofthe general type described by Telfair, et al., in patent applicationsSer. No. 938,633 and Ser. No. 009,724. When the fold mirror 42 isremoved from the beam, the present corneascope-type topography measuringdevice can be used to evaluate the contour of the cornea 28 located hearthe center of curvature of the array 11. If a beamsplitter is used inlieu of the mirror 42, the diagnostic function can be accomplished innear-real time with laser sculpturing. In either of these events, asynchronizing connection 50 is shown between the sculpturing apparatus61 and the photosensitive device 19 of the topography measuringapparatus, to assure at least an interlaced separation of sculpturingversus measuring functions in the course of a given surgical procedure.

Inasmuch as the image formed by lens 32 on photo-detecting means 19 isnot limited to the specific 5 to 7 millimeter diameter area of interestin diagnostic evaluation of the topography of the cornea, the describedapparatus can be used to observe a large portion of the exterior of theeye under magnification, as in a surgical microscope.

As depicted in FIG. 8, the field of view of the optical system isdetermined by the angular subtense of the sensitive area 43 onphotodetector 19, as measured from the center of the aperture stop 34.Typically, the extent 44 of said field of view at the eye underexamination is 12 to 16 millimeters in diameter, depending upon thespecific combination of parameters in the design.

The image of the eye is presented in real time to the observingophthalmologist and to other interested parties via the video subsystemcomprising the vidicon or CCD array 19, signal switch 21 and display 22.Illumination of the eye is provided by a light source 45 which will beunderstood to be a single lamp or a multiplicity of lamps, e.g., roomlights. By use of appropriate video components, the display can bepresented in monochrome (i.e., black and white) or in true or falsecolor.

Inherent in successful functioning of the invention is establishment ofthe proper axial distance d₁ (see FIG. 3) between the light source 11and the surface under test 28. Mathematical analysis clearly shows that,in order to achieve ±1/4 diopter precision in corneal refractive powermeasurements, the dimension d₁ must be held constant withinapproximately ±0.25 mm of the design value during calibration andoperation.

This level of distance measurement and control can be achieved in avariety of ways. For example, a simple mechanical probe of calibratedlength can be extended from the topography measuring apparatus to justtouch the surface 28 at its axial vertex when said surface is at theproper location. The possibility of damaging the test surface with aprobe precludes its application to ophthalmic applications.Non-contacting (optical or electro-optical) means such as onesfunctioning in a rangefinding mode in cameras to establish focus ormeans using inclined projected light beams which superimpose whenincident upon the test surface if said surface is located at the proper(precalibrated) axial distance or means which illuminate a multi-elementdetector array by reflected specular or scattered light can typically beapplied here.

A simple, preferred, non-contacting means for focus sensing employs anoptical microscope (commonly called a "telemicroscope") with a longworking distance, i.e. the clearance between object observed and thenearest surface of the microscope, so oriented as to allow the surface28 to be seen in profile from a direction normal to the optical axis ofthe topography measuring apparatus. By attaching this telemicroscope tothe topography measuring apparatus in stable fashion, so its line ofsight does not change location with time, it can be utilized as a fixedreference for focus distance measurement. The telemicroscope can also beused to establish the proper focus distance to either the calibrationball 70 or to the tested surface 28 to ensure applicability of thecalibration to the specific test surface evaluation.

FIG. 9 illustrates schematically one embodiment of the focus alignmentsensing device 51, i.e. a telemicroscope, integrated into the cornealtopography measuring apparatus 35. In this embodiment, means areprovided for the user's eye 53 to observe a view along the axis 27 ofthe reflected pattern of LED images from surface 28' via beamsplitter52, lens 54, mirror 55A, and eyepiece 56. Alignment reference isachieved by internal means such as a cross-hair reticle pattern 57located at the image of the LED pattern. In use during calibration, thisoptical subsystem allows the surface 28' to be centered vertically andhorizontally through action of adjustable fixture 36. In use duringmeasurement of a cornea, this subsystem provides a reference forvertical and horizontal alignment of the vertex of the eye throughaction of appropriate mechanisms which adjust position of the subject'shead and/or eye.

Another feature of the apparatus shown in FIG. 9 is the alternatetelemicroscope path formed by movement of mirror 55A out of theabove-described optical path to a position such as is shown at 55B. Animage of a side view of surface 28' or of the surface under test willthen be accessed by means of mirror 58 and lens 59 used in conjunctionwith the remaining components of the basic telemicroscope. Theappearance of the field of view of said adapted telemicroscope in thefocus measurement mode during calibration is illustrated schematicallyin FIG. 10. A similar view showing proper alignment of the eye cornea tothe telemicroscope's crosshair pattern is shown in FIG. 11. It should benoted that it is preferable, but not essential, that the image presentedto the operator's eye be erect since this would facilitate use of thedevice.

FIG. 12 represents one embodiment of an image-erecting focus alignmentmeasuring telemicroscope means 60 incorporated by mechanical structure,not shown, into a laser sculpturing apparatus 61 which is equipped witha corneal topography measuring apparatus of the type described here.

While the present invention has been described primarily for use inmeasuring the contour of a cornea, it can also be used to measure theshape of any regular or irregular contoured surface. For example, theinvention could be used to measure the contour of optical lenses,mirrors, ball bearings and precision machine parts, to name a few.

The patents and patent applications set forth in this application areintended to be incorporated by reference herein.

It is apparent that there has been provided in accordance with thisinvention a method and apparatus for measuring the topography of acontoured surface which satisfies the objects, means, and advantages setforth hereinabove. While the invention has been described in combinationwith the embodiments thereof, it is evident that many alternatives,modifications, and variations will be apparent to those skilled in theart in light of the foregoing description. Accordingly, it is intendedto embrace all such alternatives, modifications, and variations as fallwithin the spirit and broad scope of the appended claims.

I claim:
 1. A contour measuring apparatus to measure thethree-dimensional contour of a surface, comprising:a multi-point lightsource to direct a plurality of individual light beams eachcorresponding to individual light points of the multi-point light sourceonto the surface being measured; a photodetector receiving reflectionsof the individual light beams from the measured surface for generatingelectrical output signals corresponding to electro-optically measurableoptical images, each of said images corresponding to one of said lightpoints; means disposed between said surface being measured and saidphotodetector for focusing the reflected beams of light from the surfacebeing measured onto the photodetector to form the measurable opticalimages; means between the focusing means and said photodetector forcontrolling the size of the area on the measured surface from which thebeams of light are reflected; means receiving said electrical outputsignals from said photodetector for measuring the position of eachoptical image in the photodetector and for determining both the localradius of curvature of the measured surface at each point of incidenceof the individual corresponding light beams and the average radius ofcurvature of the measured surface.
 2. The contour measuring apparatus ofclaim 1 wherein said means for controlling the size of the area furthercomprises means for limiting the cone angle of the rays of theindividual light beams reflected from the measured surface whereby eachof said reflected rays closely approximates a telecentric principal raycorresponding to a light point.
 3. The contour measuring apparatus ofclaim 2 wherein said means for controlling the size of the areacomprises a telecentric aperture stop having an effective aperture of nolarger than f/13.
 4. The apparatus of claim 3 in which said telecentricaperture stop is positioned between said lens and said photodetectorsubstantially at the focal point of said lens.
 5. The apparatus of claim4 wherein the focusing means comprises a lens having and optical axisextending therethrough; andsaid photodetector includes a photodetectorsurface into which said reflected light beams are focused, saidphotodetector surface being disposed transverse to said optical axis. 6.The apparatus of claim 5 further including means to determine and storein memory the location of each individual light point on saidmulti-point light source.
 7. The apparatus of claim 6 wherein said meansto determine and store include a frame grabber.
 8. The apparatus ofclaim 7 wherein said means to determine both the local radius ofcurvature and the average radius of curvature comprises a computer. 9.The method of measuring the three-dimensional contour of a surface,comprising the steps of:directing a plurality of individual light beamseach corresponding to individual light points of a multi-point lightsource onto the surface being measured; reflecting the individual lightbeams from the measured surface onto a photodetector for generatingelectrical output signals corresponding to electro-optically measurableoptical images, each of said images corresponding to one of said lightpoints; focusing the reflected beams of light from the surface beingmeasured onto the photodetector to form the measurable optical images;controlling the size of the area on the measured surface from which thebeams of light are reflected; measuring the position of each opticalimage in the photodetector; and determining both the local radius ofcurvature of the measured surface at each point of incidence of theindividual corresponding light beams and the average radius of curvatureof the measured surface.
 10. The method of claim 9 wherein the step ofcontrolling the size of the area further includes the step of limitingthe cone angle of the rays of the individual light beams reflected fromthe measured surface whereby each of said reflected rays closelyapproximates a telecentric principal ray corresponding to a light point.11. The method of claim 10 wherein the step of controlling the sizefurther includes the step of directing the reflected rays of theindividual light beams through a telecentric aperture stop having aneffective aperture of no larger than f/13.
 12. The method of measuringthe local radii of curvature (R₁)₁ and optical powers (P₁)₁ at i pointswith coordinates (X₁, Y₁)₁ of a three-dimensional contour on a surfacebeing measured, including the steps of:locating the center of curvatureof the surface substantially on the optical axis of a contour measuringapparatus; directing a plurality of individual light beams, eachcorresponding to individual light points of a multi-point light sourceon a concave, substantially spherical surface onto the convex surfacebeing measured; receiving reflections of the individual light beams fromsaid surface on a photodetector; generating electrical output signalscorresponding to positional relationships of optical images of saidlight points; determining the radial distances (Y₁)₁ from said opticalaxis to each of the i images of the array of i light points located atpoints with known coordinates (X₂,Y₂)₁ on the concave, substantiallyspherical surface of radius R₂ centered on said optical axis and locatedat a known distance d₁ measured along the optical axis in front of theconvex surface; measuring the (X₁)₁ coordinates for these same i imagesfrom the equation: ##EQU5## where: A=(Y₁)₁ -(Y₂)₁ B=(X₂)₁ -(X₁)₁D=A[2(Y₁)₁ -A] E=2A[AX_(c) -X_(c) (Y₂)₁ -(X₂)₁ (Y₁)₁ ] G=A² [(Y₁)₁ ²-X_(c) ² ]+2AX_(c) X₂ Y₁ X_(c) =d₁ +(R₁)_(1') (R₁)_(1') =assumedapproximate value for this parameter; and measuring by successiveapproximations, the local radius (R₁)₁ from the equation: ##EQU6## 13.The method of claim 12 including the step of measuring by successiveapproximations, the local optical power (P₁)₁ (in diopters) from theequation:

    (P.sub.1).sub.1 =1000(N-1)/(R.sub.1).sub.1

where: N=index of refraction of the material on which the surface underevaluation is located.
 14. The method of claim 12 further including thestep of limiting the cone angle of the rays within the individual lightbeams reflected from the convex surface to be measured whereby theserays closely approximate a telecentric principal ray corresponding to anindividual light point and limit the area intercepted on said surface toa small localized area.
 15. The method of claim 13 further including thestep of focusing the reflected light beams from said surface onto thephotodetector to form measurable optical images.
 16. The method of claim15 further including the step of measuring the position of each opticalimage formed on the photodetector.
 17. The method of measuring thecoordinates (X₂)₁, (Y)₁ of each light point of the contour measuringapparatus of claim 12, including the steps of:substituting a generallyspherical calibration surface of known radius of curvature R₂ in lieu ofthe surface being measured; measuring the radial distances (Y₁)₁ fromthe optical axis to each of the i images of said array of i point lightpoints using the following equations:

    K.sub.1 =(X.sub.c -X.sub.1)Y.sub.1.sup.2

    K.sub.2 =(X.sub.1 -X.sub.c)Y.sub.1

    K.sub.3 =Y.sub.1.sup.2 -X.sub.c.sup.2 +2X.sub.c X.sub.1 -X.sub.1.sup.2

    K.sub.4 =2(X.sub.c.sup.2 Y.sub.1 -X.sub.c X.sub.1 Y.sub.1 -Y.sub.1.sup.3)

    K.sub.5 =Y.sub.1.sup.4 +X.sub.1.sup.2 Y.sub.1.sup.2 -X.sub.c C.sup.2 Y.sub.1.sup.2

    H=4K.sub.2.sup.2 +K.sub.3.sup.2

    I=(4K.sub.2 K.sub.3 R.sub.2 +2K.sub.3 K.sub.4 +8K.sub.1 K.sub.2)/H

    J=(4K.sub.1.sup.2 +4K.sub.1 K.sub.3 R.sub.2 +4K.sub.2 K.sub.4 R.sub.2 +2K.sub.3 K.sub.5 +K.sub.4.sup.2)/H

    L=(4K.sub.1 K.sub.4 R.sub.2 +4K.sub.2 K.sub.5 R.sub.2 +2K.sub.4 K.sub.5)/H

    M=(4K.sub.1 K.sub.5 R.sub.2 +K.sub.5.sup.2)/H

    Y.sub.2.sup.4 +IY.sub.2.sup.3 +JY.sub.2.sup.2 +LY.sub.2 +M=0 ##EQU7##


18. An apparatus to measure the three-dimensional contour of a surface,comprising:a contour measuring device having an optical axis extendingtherethrough, said contour measuring device comprising: means to directlight beams onto the surface being measured; means for receivingreflections of said light beams from the surface being measured; meansconnected to the reflection receiving means for measuring the contour ofsaid surface; means for positioning the surface being measured withrespect to the reflection receiving means to establish a desired axialdistance therebetween; said means for positioning comprising an opticalmicroscope attached to said contour measuring device so that a line ofsight extending outwardly from said optical microscope is perpendicularto the axis through said contour measuring device and substantiallytangent to the surface being measured.